Distributed resource allocation: an indirect dual ascent method with an exponential convergence rate
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ORIGINAL PAPER
Distributed resource allocation: an indirect dual ascent method with an exponential convergence rate Wen-Ting Lin · Yan-Wu Wang Xinghuo Yu
· Chaojie Li ·
Received: 30 May 2019 / Accepted: 15 November 2019 © Springer Nature B.V. 2020
Abstract In this paper, an indirect dual ascent method with an exponential convergence rate is proposed for a general resource allocation problem with convex objectives and weighted constraints. By introducing the indirect dual variables, the dual dynamics can be executed in a decentralized manner by all nodes over the network. In contrast to the conventional methods, consensus on all the dual variables is not required. This further leads to the fast convergence, reduced communication burden and better privacy preserving. Moreover, the exponential convergence rate of the proposed algorithm is established through the Lyapunov method and the singular perturbation theory. Application of the Submitted to Nonlinear Dynamics, May 2019. W.-T. Lin · Y.-W. Wang (B) School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] W.-T. Lin · Y.-W. Wang Key Laboratory of Image Processing and Intelligent Control (Huazhong University of Science and Technology), Ministry of Education, Wuhan, China W.-T. Lin e-mail: [email protected] C. Li School of Electrical Engineering and Telecommunications, UNSW, Kingston, NSW 2052, Australia e-mail: [email protected] X. Yu School of Engineering, RMIT University, Melbourne, VIC 3000, Australia e-mail: [email protected]
dynamic power dispatch problem in smart grid verifies the effectiveness and performance of the proposed algorithm. Keywords Resource allocation · Dual ascent dynamics · Distributed algorithm · Exponential convergence
1 Introduction 1.1 Motivation and related works Resource allocation problem is extensively investigated due to its increasing applicability across a large variety of disciplines such as smart grid (e.g., [1– 3]), wireless and social networks (e.g., [4–6]) and robotics (e.g., [7–10]). In the resource allocation problem, the participants have preference over the alternative resources and participate in the decision making with the supply–demand balance constraint. From the perspective of optimization, the resource allocation problem can be modeled as an optimization problem with globally coupled constraints, which can be solved by a wide range of optimization methods. One efficient approach for solving the resource allocation problem is the centralized optimization method, where a central decision maker makes the allocation decision with all the network information and then sends the decisions to corresponding participants. Though the centralized optimization method seems available, scal-
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ability is a challenging problem when applied to largescale systems. Moreover, since all the network information needs to be delivered to the central decision maker, it also leads to privacy issues. Owing to the developm
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